Research On Spatial Signal Processing Of Conformal Array Based On Geometric Algebra

Array signal processing has played a vital role in many diverse application areas,such as radar, radio astronomy, communications and seismology. Most modern radar,communication and sonar systems depend on antennas, detectors or other sensingdevice arrays as an indispensable component of the system. Theories and algorithmsbased on linear or planar arrays, especially for uniform linear arrays (ULA), are nowmature given over forty years' development. However, there is little literatureconcerning conformal arrays with complex geometric structure. Proceeding from thecharacteristic that differentiates between traditional linear or planar arrays andconformal arrays, this dissertation establishes the analysis model for conformal arrays,using the powerful mathematical technique, Geometric Algebra, as the basis ofconformal array analysis. Based on the model and analysis, we present novel andsignificant research on pattern analysis&synthesis of conformal arrays, beamforming,and direction-of-arrival estimation; theoretical analysis and simulation experiments areperformed to demonstrate the effectiveness of the proposed methods. The maincontributions of the dissertation are addressed individually below:First of all, geometric algebra is introduced in detail, with emphasis on theadvantages for conformal array analysis of using this mathematical framework.Secondly, the thesis presents the conventional array signal processing model.Starting from the particular characteristics of conformal arrays, difficulties in analyzingconformal arrays with complex configuration based on the traditional model are pointedout and we also summarize the classical analytical method using Euler rotation matrices.Mathematical modeling and analysis methods for arbitrary conformal arrays withcomplex configuration are then obtained. We also acquire three-dimensional patterns forarbitrary array structure with directional and polarized elements, and contrast theproposed method with traditional methods. Via the 'mutual coupling compensationmatrix', the proposed analysis model and other subsequent methods clarified in thisdissertation can be readily extended to actual applications that take mutual couplingeffects into account. Thirdly, in order to handle beamforming for a cylindrical array with directionalelements, we introduce the idea of subarray division to obtain a beamformer based onthe conventional minimum variance distortionless response (MVDR) algorithm. Usingthe geometric algebra analysis model, we study beamforming and pattern shaping ofconformal arrays, combined with the traditional beamforming method and convexoptimization theory. Simulation results show those proposed algorithms can beeffectively used for three-dimensional pattern shaping.Fourthly, based on the analysis method of geometric algebra, we use theintersection approach to three-dimensional pattern synthesis of conformal arrays.Pattern synthesis methods for arbitrary geometry are hence derived and simulated inMATLAB.Lastly, for conformal arrays with symmetrical structure, we use the estimation ofsignal parameters via rotational invariance techniques (ESPRIT) algorithm to correct theconformal array model iteratively, and realize the direction-of-arrival and the state ofpolarization estimates. The feasibility and validity of the method are proved viasimulation results.